1. Field of the Invention
This invention relates to a method and a circuit for determining the impulse response of a broad band linear system. More specifically, the invention relates to a method in which the impulse response of such a system can be determined in the high frequency range at approximately 100 MHz to 10 Ghz. Specifically, this invention also provides a method for the determining the impulse response of multi-channel broad band linear systems. The invention, furthermore, provides a circuit for carrying out such methods.
2. The Prior Art
In electrical and electronics engineering the transmission characteristics of linear systems are, for example, determined and characterized by the impulse response g(t) or, respectively, the transfer function G(f). The term linear system means any system in which the output magnitudes y(t) are to the input magnitudes x(t) in a relation which is defined as follows: EQU y(t)=.intg.g(.tau.)x(t-.tau.)d.tau. 1
Y(.function.)=G(.function.)X(.function.) 2
In systems with an input x and an output and scalar equations result, while in the case of systems having a plurality of inputs and outputs are described by matrix relations. The impulse response g(t) or, respectively the transfer function G(f) are representative of the characteristics of the system under consideration.
In the development, manufacture, and research of any desired technical system, particularly of UWB sensors (ultra wideband sensors) and sensor arrays, the metrological determination of the impulse response or, respectively of the transfer function becomes a substantial question.
In the state of the art for the metrological determination of the impulse response or, respectively, for the transmission function, there are three basic principles in use. In the so- called pulse metrological technique, all inputs of the system which are under investigation are respectively controlled with a small impulse and the output signals are measured at all outputs of the systems. In the ideal case, Dirac pulse is used. When the above mentioned integral equation (1) is solved, the impulse response of the system can be determined. The particular difficulties of this method are that a rather steep input impulse with a high voltage needs to be applied at the inputs, so as to largely eliminate potentially present interferences. Measuring systems, which operate in the region of interest in the high and highest frequency range when using the impulse determination method, provide only a low measuring speed, and requires a substantial amount of equipment.
A second method which is in practical use is the so-called sinus measuring technique wherein test signals are introduced into the system under study comprised of a multiplicity of sinusoidal vibrations of varying frequencies. Due to the required large number of varying frequencies in the test signals, this technique is slow and requires a large amount of equipment.
As a third method there is known the correlation measuring technique. In contrast to the impulse and sinus measuring techniques, any desired signal wave forms can be introduced as a test signal, provided their band width is sufficiently large. In contrast to the sinus measuring technique, all determinations and considerations are done not in the frequency range but in the respective time range. Between the correlation functions for systems with K inputs and L outputs the following relationships apply: EQU .psi..sub.xy (.tau.)=.intg.g(.xi.).psi..sub.xx (.xi.=.tau.)d.xi. (3) EQU with EQU .psi..sub.xy (.tau.)=.intg.y(t)x.sup.T (t+.tau.)dt [L,K]--Matrix EQU .psi..sub.xx (.tau.)=.intg.x(t)x.sup.T (t+.tau.)dt.apprxeq..delta.(.tau.)D [K,K]--Matrix EQU xis the Transponent of x. EQU x(t)=[x.sub.1 (t),x.sub.2 (t), . . . , x.sub.K (t)].sup.T --Vector for the input signals EQU y(t)=[y.sub.1 (t),y.sub.2 (t), . . . , y.sub.L (t)].sup.T --Vector for the output signals EQU D--Diagonal matrix
As test signals these signals are to selected as the auto-correlation matrix which is most closely related to a diagonal matrix of Dirac functions.
The required demands of the UWB correlation methods are fulfilled by known systems only partially or with a great deal of effort. Furthermore, it is desirable that the band width which is applied to the system, can be varied in a simple manner, with one and the same measuring device, to evaluate differing systems, or respectively, differing characteristics of the same system in varying frequency ranges. Since such requirements cannot be fulfilled with known correlation measuring methods, correlation measuring methods were employed only on a limited scale, in the metrology of high frequency systems.
In the paper: "Applications of the Maximal Sequence Measuring Technique in Acoustics'" by M. Vorlander, which appeared in the symposia publications "Advances in Acoustics--DAGA 94" in Bad Honnef: DPG GmbH 1994, there is provided a correlation measuring method. This measuring method uses a maximum length binary sequences (MLBS) as a stimulation signal for the device under test. The output signal is subjected to a Hadamard transformation to furnish the desired impulse response. From the output signals generated from the impulse response, these are subjected to a Hadamard-transformation as input signals for the system under investigation. From this article, the convolution integral of the correlation measuring technique is also known in its general form. ##EQU1##
There is an advantage from the correlation measuring technique wherein the instigating signal per se need not be similar to a Dirac input, but it should be its auto-correlation function. This is particularly useful with respect to the control of the system and the signal/noise ratio. Periodic binary random noise signals are referred to MLBS with an auto- correlation function, which is close to a Dirac input.
The aforementioned article shows the application of a correlation measuring technique, particularly the MLBS measuring technique in the domain of acoustics. With the known method and the respective apparatus, however, no measurements can be carried out in the high frequency range.
In the dissertation of H. Alrutz with the title "Concerning the application of random noise sequences for measuring of liner transmission systems," Gottingen, 1983, inter alia the possibility is also discussed of utilizing MLBS as test signals for measuring in the high frequency range. Thereby, a MLBS generator is proposed which employs two shift registers, and a fast comparator. With this arrangement the MLBS can be synchronized with a sample clock pulse whereby it is possible to have one sampling only per period of the MLBS. Multi-sampling within a period, which are a prerequisite for the increase in velocity/speed, can not be carried out, Furthermore the cascading of several measuring units is difficult.
In German Patent 4209761 A1 there is described a method for the determination of the transmission characteristics of an electrical system. In the system under investigation a test signal is introduced, the auto-correlation function of which is a delta pulse. At the output the received signal is evaluated in the manner so that it is cross-correlated with a reference signal. The output signal then is representative of the transmission characteristics of the system. This method is mainly used for the investigation of line/conduction characteristics and is not applicable for the fast measuring of multi-channel systems.